I have a table created with this query.

CREATE TABLE `example` (

  `a` int(11) DEFAULT NULL,

  KEY `a` (`a`)

) ENGINE=InnoDB;

This table contains data:

INSERT INTO `example` VALUES (1),(2);

When I am trying to run two queries at the same time from the different connections I've got Deadlock.
Console1:

SET autocommit=0; SET SESSION TRANSACTION ISOLATION LEVEL SERIALIZABLE;start transaction;select a from example where a=4;

Console2:

SET autocommit=0; SET SESSION TRANSACTION ISOLATION LEVEL SERIALIZABLE;start transaction;select a from example where a=4;

After transaction is started I am running the following in both consoles:

insert into example (a) values (4);

But if I use a=0 or for example a='v' in WHERE clause deadlock doesn't occur.

I attached docker-compose and test.sh script to demonstrate this issue.
test.sh runs two queries from specified file as two different processes 1000 times by default.
Files named deadlocks_[1,2,3] contains queries causes deadlocks.
Just run

docker compose up -d

./test.sh local deadlocks_1

And you will get something like

ERROR 1213 (40001) at line 1: Deadlock found when trying to get lock; try restarting transaction
Failed runs: 347

But

./test.sh local no_deadlocks_1

will print

Failed runs: 0